The cold classical Kuiper Belt Objects (KBOs) possess a high, $gtrsim30%$ binary fraction. Widely separated and dynamically fragile, these binary systems have been useful in tracing the origins of KBOs. A new class of binaries was recently identified by their colours. The so-called blue binaries are unanimously members of the less red compositional class, and exhibit a 100% binary fraction. They appear to be push-out survivors, emplaced in the classical region during Neptunes phases of outward migration. The presence of these binary systems implies that the majority of objects that formed near the cold classical region formed as binaries. Here we present new optical colour measurements of cold classical KBOs from the Colours of the Outer Solar System Origins Survey, including colours of a blue binary discovered by the Solar System Origins Legacy Survey -- 2015 RJ277. The increased size of the colours sample has resulted in order-of-magnitude decrease in the probability that the binaries and singles sample share the same colour distribution. From the Anderson-Darling statistic, this probability is only a 0.3%, while it is only 0.002% when utilizing the difference of means statistic. We find a hint that the blue binaries have inflated free inclinations compared to their red counterparts, consistent with the push-out origin for these bodies.